Heretofore, when analogue data are created from discrete data such as digital data, Shannon's sampling function has been extensively utilized which was derived based on Shannon's sampling theorem. Here, the Shannon's sampling function becomes equals to 1 only at a sample point t=0 as shown in FIG. 22 and becomes 0 at all the other sampling points, exhibiting a waveform whose vibration theoretically continues to infinity from −∞ to +∞. Accordingly, when utilizing various processors to actually perform an interpolation process among discrete data using Shannon's sampling function, the interpolation process is forcibly truncated within a finite interval. As a result, there has been the issue that an error was generated due to the truncation.
Further, when utilizing such a Shannon's sampling function, since analogue signals reproduced were subjected to band limitation, when discrete data recorded on. e.g., a CD (Compact Disc) and a DVD (Digital versatile Disc) were converted into analogue signals to be reproduced, high frequencies not less than 22.5 KHz were unable to reproduce, posing the issue that natural sounds containing the sounds with frequencies not less than 22.5 KHz could not be reproduced.
Here, to solve such an issue, the error due to the truncation does not occur and therefore a sampling function has been evolved which is capable of reproducing farther higher frequency range components and converges within a finite range (e.g., see patent document 1). This sampling function converges to 0 at the second sampling positions anteroposterior to the original point and hence signal reproduction can be performed with a small amount of calculations, thus making it possible to ascertain that farther higher-frequency range d is contained.    Reference document 1: International unexamined patent application publication No. 99/38090